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NumericalAlgebraicGeometry :: randomSd(List)

randomSd(List) -- a random homogeneous system of polynomial equations

Synopsis

Description

Generates a system of homogeneous polynomials Ti such that deg(Ti) = di. The system is normalized, so that it is on the unit sphere in the Bombieri-Weyl norm.

i1 : T = randomSd {2,3}

                                 2                                       
o1 = {(- .0480647 - .113595*ii)x1  + (- .00623084 - .285074*ii)x1*x2 + (-
     ------------------------------------------------------------------------
                            2                                            
     .086036 + .116567*ii)x2  + (.133897 - .0738777*ii)x1*x3 + (.580688 +
     ------------------------------------------------------------------------
                                                 2             
     .586331*ii)x2*x3 + (.229687 - .0151083*ii)x3 , (.0841534 +
     ------------------------------------------------------------------------
                  3                              2               
     .213392*ii)x1  + (- .0349711 + .170314*ii)x1 x2 + (.498678 +
     ------------------------------------------------------------------------
                     2                            3               
     .370848*ii)x1*x2  + (.209191 - .0511848*ii)x2  + (- .454972 -
     ------------------------------------------------------------------------
                  2                                                  
     .172011*ii)x1 x3 + (.403134 - .398683*ii)x1*x2*x3 + (- .113378 +
     ------------------------------------------------------------------------
                  2                                2               
     .136155*ii)x2 x3 + (.199468 + .430145*ii)x1*x3  + (- .245619 -
     ------------------------------------------------------------------------
                       2                            3
     .00304687*ii)x2*x3  + (.192521 - .0717185*ii)x3 }

o1 : List
i2 : (S,solsS) = goodInitialPair T;
i3 : M = track(S,T,solsS,gamma=>0.6+0.8*ii,Software=>M2)

o3 = {{-.262757+.323869*ii, -.20867+.042039*ii, .87219+.141572*ii}}

o3 : List

See also